The Dupuit approximation (see [1]}, Chapter 8) defines volumetric groundwater flux \(\mathbf {\mathit {q}}\)  in an unconfined aquifer when the flow is essentially horizontal. In this case, the piezometric head \(\psi \)  is vertically uniform and the usual form of Darcy's law, \(q = -K \nabla \psi \) , can be expressed in terms of the water table \(h\) , which is the height of the free surface at the top of the saturated zone.
\(\mathbf {\mathit {q}}(x,y,z) = -K(x,y,z) \nabla h(x,y)  \, ,\) 
